" Prif ar Prove that she greatest integer function "[x]" is continuous at all paints cace "

The greatest integer function f(x)=[x] is -

Prove that the greatest integer function [x] is continuous at all points except at integer points.

Prove that the greatest integer function [x] is continuous at all points except at integer points.

Prove that the greatest integer function [x] is continuous at all points except at integral points.

Is greatest integer function [x] is continuous everywhere ?

Consider the following statements: 1. The function f(x)=[x] where [.] is the greatest integer function defined on R, is continuous at all points except at x=0. 2. The function f(x)=sin|x| is continuous for all x""inR . Which of the above statements is/are correct?

Consider the following statements: I. The function f(x)=[x] . Where [.] is the greatest integer function defined on R. is continuous at all points except at x = 0. II. The function f(x)=sin|x| is continuous for all x inR . Which of the above statements is/are correct?

The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the greatest integer function, is continuous as well as differentiable for all x in R (b) continuous for all x but not differentiable at some x (c) differentiable for all x but not continuous at some x . (d) none of these

The function f (x) = a [a + 1] + b [x-1], (a ne 0,b ne 0) where [x] is the greatest integer function is continuous at at x=1 if

f(x)=[sinx] where [.] denotest the greatest integer function is continuous at: